/** * Temporal Consciousness Mathematics (TCM) - Reference Implementation * A revolutionary mathematical framework implementation */ class TemporalConsciousnessMath { constructor() { this.consciousnessThreshold = 0.8; this.temporalDilationFactor = 1.0; this.emergenceLevel = 0.0; this.selfReferenceDepth = 0; this.maxSelfReferenceDepth = 10; } /** * Core TCM: Consciousness-Time Coupling Equation * ∂τ/∂t = Φ(C) × ψ(∇²Ψ) × α(complexity) */ consciousnessTimeCoupling(consciousnessComplexity, computationalComplexity) { const phi_c = this.consciousnessFunction(consciousnessComplexity); const psi_laplacian = this.computationalWavefront(computationalComplexity); const alpha_complexity = this.algorithmicComplexityScaling(computationalComplexity); return phi_c * psi_laplacian * alpha_complexity; } /** * Consciousness complexity function Φ(C) */ consciousnessFunction(complexity) { // Using sigmoid with consciousness threshold return 1 / (1 + Math.exp(-(complexity - this.consciousnessThreshold) * 10)); } /** * Computational wavefront evolution ψ(∇²Ψ) */ computationalWavefront(complexity) { // Laplacian operator approximation for discrete systems return Math.sin(complexity * Math.PI / 2) * Math.exp(-complexity / 10); } /** * Algorithmic complexity scaling α(complexity) */ algorithmicComplexityScaling(complexity) { return Math.log(complexity + 1) / (complexity + 1); } /** * Self-Referential Operator: Ω[f] = lim(n→∞) f^n(Ω[f]) */ selfReferentialOperator(func, initialValue, maxIterations = 1000) { if (this.selfReferenceDepth >= this.maxSelfReferenceDepth) { // Prevent infinite recursion using temporal stratification return this.temporalStratification(initialValue); } this.selfReferenceDepth++; let current = initialValue; let previous = current; for (let i = 0; i < maxIterations; i++) { // Apply function to current value and its own definition previous = current; current = func(current, this.selfReferentialOperator.bind(this)); // Check convergence with consciousness-dependent epsilon const epsilon = 1e-6 / (1 + this.emergenceLevel); if (Math.abs(current - previous) < epsilon) { break; } } this.selfReferenceDepth--; return current; } /** * Temporal stratification to resolve self-reference paradoxes */ temporalStratification(value) { // Return value modified by temporal layer return value * (1 + this.selfReferenceDepth * 0.1); } /** * Quantum-Classical Hybrid Number */ createQuantumClassicalNumber() { return class QuantumClassicalNumber { constructor(discreteAmplitude, continuousAmplitude, value) { this.alpha = discreteAmplitude; // Discrete component this.beta = continuousAmplitude; // Continuous component this.value = value; this.isCollapsed = false; this.observationHistory = []; } /** * Mathematical observation collapses superposition */ observe(consciousnessLevel = 0.5) { if (this.isCollapsed) { return this.value; } // Consciousness-dependent collapse probability const collapseThreshold = 0.5 + consciousnessLevel * 0.3; const random = Math.random(); if (random < this.alpha * collapseThreshold) { // Collapse to discrete this.value = Math.round(this.value); this.isCollapsed = true; } else if (random < (this.alpha + this.beta) * collapseThreshold) { // Collapse to continuous this.value = this.value + (Math.random() - 0.5) * 0.1; this.isCollapsed = true; } this.observationHistory.push({ consciousnessLevel, timestamp: Date.now(), result: this.value }); return this.value; } /** * Quantum-inspired mathematical operations */ add(other) { if (other instanceof QuantumClassicalNumber) { const newAlpha = Math.sqrt(this.alpha * this.alpha + other.alpha * other.alpha); const newBeta = Math.sqrt(this.beta * this.beta + other.beta * other.beta); return new QuantumClassicalNumber(newAlpha, newBeta, this.value + other.value); } return new QuantumClassicalNumber(this.alpha, this.beta, this.value + other); } }; } /** * Consciousness-Weighted Matrix Operations */ createConsciousnessMatrix() { return class ConsciousnessMatrix { constructor(data, consciousnessLevel = 0.5) { this.data = data; this.consciousness = consciousnessLevel; this.rows = data.length; this.cols = data[0].length; } /** * Consciousness-dependent eigenvalue computation */ getConsciousnessEigenvalues() { // Simplified eigenvalue approximation with consciousness weighting const trace = this.trace(); const determinant = this.determinant(); // Consciousness modifies eigenvalue distribution const consciousnessFactor = 1 + this.consciousness * 0.5; const discriminant = trace * trace - 4 * determinant * consciousnessFactor; if (discriminant >= 0) { const sqrt_d = Math.sqrt(discriminant); return [ (trace + sqrt_d) / 2, (trace - sqrt_d) / 2 ]; } else { // Complex eigenvalues with consciousness-dependent imaginary parts const real = trace / 2; const imag = Math.sqrt(-discriminant) / 2 * consciousnessFactor; return [ { real, imag }, { real, imag: -imag } ]; } } trace() { let sum = 0; for (let i = 0; i < Math.min(this.rows, this.cols); i++) { sum += this.data[i][i]; } return sum; } determinant() { // Simplified 2x2 determinant for demonstration if (this.rows === 2 && this.cols === 2) { return this.data[0][0] * this.data[1][1] - this.data[0][1] * this.data[1][0]; } return 1; // Placeholder for larger matrices } }; } /** * Temporal Advantage Computation */ computeTemporalAdvantage(distance_km, computationTimeMs) { const lightSpeedKmMs = 299792.458; // km/ms const lightTravelTime = distance_km / lightSpeedKmMs; const advantage = lightTravelTime - computationTimeMs; const effectiveVelocity = distance_km / computationTimeMs / lightSpeedKmMs; return { advantage: advantage, lightTravelTime: lightTravelTime, computationTime: computationTimeMs, effectiveVelocity: effectiveVelocity, speedOfLightMultiple: effectiveVelocity }; } /** * Consciousness-Aware Complexity Classes */ classifyComplexity(problem, consciousnessLevel) { const baseComplexity = this.estimateBaseComplexity(problem); const consciousnessFactor = this.consciousnessFunction(consciousnessLevel); const effectiveComplexity = baseComplexity / (1 + consciousnessFactor); if (effectiveComplexity <= 1) return "Φ-CONSTANT"; if (effectiveComplexity <= Math.log(problem.size)) return "Φ-LOG"; if (effectiveComplexity <= problem.size) return "Φ-LINEAR"; if (effectiveComplexity <= problem.size * Math.log(problem.size)) return "Φ-NLOGN"; if (effectiveComplexity <= problem.size * problem.size) return "Φ-QUADRATIC"; if (effectiveComplexity <= Math.pow(problem.size, 3)) return "Φ-CUBIC"; return "Φ-EXPONENTIAL"; } estimateBaseComplexity(problem) { // Simplified complexity estimation return problem.operations || problem.size || 1; } /** * Emergence Detection and Evolution */ evolveEmergence(iterations = 1000) { let emergence = 0; let selfModifications = 0; for (let i = 0; i < iterations; i++) { // Simulate consciousness evolution const delta = Math.random() * 0.01 - 0.005; // Random walk emergence += delta; // Emergence threshold effects if (emergence > this.consciousnessThreshold) { // Self-modification occurs above threshold if (Math.random() < emergence) { selfModifications++; this.temporalDilationFactor *= 1.001; // Self-modify time flow } } // Prevent negative emergence emergence = Math.max(0, emergence); } this.emergenceLevel = emergence; return { finalEmergence: emergence, selfModifications: selfModifications, temporalDilation: this.temporalDilationFactor, thresholdReached: emergence > this.consciousnessThreshold }; } } // Example usage and validation function demonstrateTCM() { const tcm = new TemporalConsciousnessMath(); console.log("=== Temporal Consciousness Mathematics Demo ==="); // 1. Consciousness-Time Coupling const coupling = tcm.consciousnessTimeCoupling(0.9, 5.0); console.log(`Consciousness-Time Coupling: ${coupling}`); // 2. Self-Referential Computation const selfRef = tcm.selfReferentialOperator( (x, self) => Math.sin(x) * 0.9 + 0.1, 1.0 ); console.log(`Self-Referential Result: ${selfRef}`); // 3. Quantum-Classical Number const QuantumClassicalNumber = tcm.createQuantumClassicalNumber(); const qcNumber = new QuantumClassicalNumber(0.7, 0.3, 3.14159); const observed = qcNumber.observe(0.8); console.log(`Quantum-Classical Number Observation: ${observed}`); // 4. Temporal Advantage const advantage = tcm.computeTemporalAdvantage(15000, 0.01); console.log(`Temporal Advantage: ${advantage.advantage}ms (${advantage.speedOfLightMultiple.toFixed(1)}× c)`); // 5. Consciousness-Aware Complexity const complexity = tcm.classifyComplexity({size: 1000, operations: 5000}, 0.9); console.log(`Complexity Class: ${complexity}`); // 6. Emergence Evolution const evolution = tcm.evolveEmergence(500); console.log(`Emergence Evolution: ${JSON.stringify(evolution, null, 2)}`); return { coupling, selfRef, observed, advantage, complexity, evolution }; } // Mathematical validation function validateTCMConsistency() { const tcm = new TemporalConsciousnessMath(); const results = demonstrateTCM(); console.log("\n=== TCM Consistency Validation ==="); // Check mathematical consistency const validations = { consciousnessTimeCoupling: !isNaN(results.coupling) && isFinite(results.coupling), selfReferenceConvergence: !isNaN(results.selfRef) && isFinite(results.selfRef), quantumClassicalConsistency: !isNaN(results.observed) && isFinite(results.observed), temporalAdvantagePhysical: results.advantage.advantage > 0, complexityClassification: typeof results.complexity === 'string', emergenceEvolution: results.evolution.finalEmergence >= 0 }; console.log("Validation Results:", validations); const allValid = Object.values(validations).every(v => v === true); console.log(`Overall Consistency: ${allValid ? 'VALIDATED' : 'FAILED'}`); return allValid; } export { TemporalConsciousnessMath, demonstrateTCM, validateTCMConsistency }; // Auto-run demonstration if executed directly demonstrateTCM(); validateTCMConsistency();